1. Field of Invention
This invention is related generally to logical transform processors, and more specifically, to a logical transform processor that maps a three dimensional structure and surrounding space into an image that can be altered.
2. Description of the Prior Art
A planar image, such as one displayed on a cathode ray tube (CRT), is almost always regarded as being two dimensional. However, as explained hereinafter, what appears to be a three dimensional image may be made from a plurality of two dimensional images.
A CRT display of an image of a ball may be made by first displaying an image of a slice of the ball in a plane farthest from an observer. Next, a slice in the interior of the ball in a plane closer to the observer is displayed. In a similar manner, images of slices of the interior of the ball in planes of decreasing distance from the observer are displayed. When the images of the slices are displayed at a suitable rate, the observer sees what appears to be a three dimensional image of the ball.
A three dimensional image may either remain unchanged or be altered via computer processing. An example of the unchanged three dimensional image is in the field of computed tomography where a three dimensional image of an organ of an animal is provided from images in selected planes.
An example of the altered three dimensional image is in the field of computer graphics. A CRT display of a three dimensional image of a building may be altered to study how the building looks with the sun at selected elevations. Typically, the image of the building is divided into a grid structure to define a plurality of polygonal regions, each having a desired shade of grey. However, the image of the building may have an undesired patchwork appearance.
Another example of the altered three dimensional image is in the field of neurology. A CRT display of a three dimensional image of a neural network of a person or an animal may be altered by a computer process, known as skeletonizing, to facilitate the tracing of the network.
A typical three dimensional image of a scene includes a structure and surrounding space. The scene is divided into a multiplicity of least resolvable elements, known as voxels. Accordingly, a signal representation of the typical image is comprised of signals representative of all of the voxels comprising the scene. More particularly, a signal representative of an exemplary voxel is either a logic "1" signal or a logic "0" signal when the exemplary voxel is included in the structure or the space, respectively.
The processing of the signal representative of the exemplary voxel is often equivalent to comparing an array formed by the exemplary voxel and voxels proximal thereto (referred to as neighbors hereinafter) to all possible arrays. Based upon the comparison, an image of the exemplary voxel may, for example, be shaded to a selected one of a plurality of shadings.
One type of array is comprised of voxels that define a cube. Twenty-six voxels are arranged at midpoints and ends of line segments comprising edges of the cube. One voxel is at the center of the cube. Another type of array is comprised of voxels that define an octahedron. Eighteen voxels are arranged at ends of line segments comprising edges of the octahedron. One voxel is at the center of the octahedron.
All possible cubic arrays are defined by 2.sup.27 combinations of logic signals. All possible octahedral arrays are defined by 2.sup.19 combinations of logic signals. The number of combinations of signals to define all possible arrays of either the cube or the octahedron are undesirably large.
There has heretofore been a need to define a neighborhood that is easily adapted for computer processing and to implement computer processing of a three dimensional image of a multiplicity of voxels.